Mark seam breaks other uv island
I guess what you need to do is pin your UV map:


Let say you've made your first unwrap with a seam. Select all in the UV Editor and press P in order to pin.





Create your second seam.





In the object, select the part you want to unwrap again, in the UV Editor remove the pin for this part with AltP.





Unwrap again. In the UV Editor, it won't affect the pinned vertices, it will only affect the non-pinned vertices.





Move and scale the new islands wherever you want in the UV Editor.